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Question:1
Solution: Region bounded by
x = 0, x = 1 and y = x, y = 1
Now we evaluate the integral by hanging the order of integral
Question:2 The value of the double integral
Solution: Region of integration is bounded y=0, y = x and x = 0, x = π
changing the order of integration
= 2
Question:3 Evaluate
Solution:
Question4: Change the order of integration in the double integral
Solution: Domain of integration is bounded by the following curves
point of intersection of the curve y =2  x^{2} and y = x we get when
So (1,1 ) and (2,2 ) are the points of intersection.
Now the given integral modify by changing the order of integration we get
Something skip follow book
Question5: Changing the order of integration of
Solution:
The region of integration is bounded by y = 0, y = x, x = 1, x = 2 after changing the order the integration changes to
Question6: Let D the trianle bounded by the yaxis the line 2y = π. Then the value of the integral
(a) 1/2 (b) 1 (c) 3/2 (d) 2
Solution:
Question7: Change the order of integration in the integral
Solution: The domain of the double integration is bounded by the curves y = x  1,
Question8: Let I = Then using the transformation x = rcosθ, y = rsinθ, integral is equal to
Solution: Region of integration is bounded by curves
for first integral,
Question9: Evaluate integral
(a) 0 (b) 1/2 (c) 1 (d)2
Solution: Region of integration is bounded by curves
changing the order
Question 10: The value of equals
(a) π/4 (b) 1/2π (c) 1/4 (d) 1/2
Solution:
Question11: (a) Find in the area of the smaller of the two regions enclose between
Solution:
Solution (b)
The region of integration is bounded by x = 0, x = y, y = 1, y = ∞ and shown in figure changing the order
Question12: Let f , be a continuous function with
Solution: Given, be a continuous function with
Now apply change of order of integration
Domain of integration is given by graph
Question13: By changing the order of integration, the integral can be expressed as
Solution: The domain of integration is bounded y = 1, changing the order
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